Large Deviations of Products of Random Topical Operators

A topical operator on R-d is one which is isotone and homogeneous. Let {A(n) : n greater than or equal to 1} be a sequence of i.i.d. random topical operators such that the projective radius of A(n)...A(1) is almost surely bounded for large n. If {x (n) : n greater than or equal to 1} is a sequence of vectors given by x (n) = A (n)...A(1)x(0), for some fixed initial condition x(0), then the sequence {x(n)/n:n greater than or equal to 1} satisfies a weak large deviation principle. As corollaries of this result we obtain large deviation principles for products of certain random aperiodic max-plus and min-plus matrix operators and for products of certain random aperiodic nonnegative matrix operators.